Problem: Simplify the following expression: $ n = \dfrac{-10z + 7}{z + 3} + 5 $
In order to add expressions, they must have a common denominator. Multiply the second expression by $\dfrac{z + 3}{z + 3}$ $ \dfrac{5}{1} \times \dfrac{z + 3}{z + 3} = \dfrac{5z + 15}{z + 3} $ Therefore $ n = \dfrac{-10z + 7}{z + 3} + \dfrac{5z + 15}{z + 3} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{-10z + 7 + 5z + 15}{z + 3} $ $n = \dfrac{-5z + 22}{z + 3}$